When adding 1996 and 1997 – the result is 3993 –where we observe that, we add 6 and 7 first getting 3 in the first rightmost column and carrying 1 over to the second column. In the same vein, we obseve that- there are three carries in total in the said addition.

Determine the minimum value of a positive integer C such that when we add 1996*C and 1997*C, there do not arise any carry throughout the entire calculation.

Does there exist an infinite number of values of C satisfying the given conditions?
Give reasons for your answer.

If C works, then so does C*10^n.  Therefore, if there are any C that work, then there are an infinite number that work.

Posted by Steve Herman on 2016-04-26 12:25:05